Stability of monotone travelling waves for competition-diffusion equations
- 110 Downloads
We consider the Lotka-Volterra competition model with diffusion inR, and establish a theorem on the asymptotic stability of monotone travelling waves relative to the space of bounded uniformly continuous functions with the supremum norm. In consideration of the result of Alexander et al.  and Derndinger , we shall arrive at a study of the non-negative eigenvalues of the linearized operator around the travelling wave.
Key wordscompetition-diffusion system travelling wave stability
- P. W. Bates and C. K. R. T. Jones, Invariant, manifolds for semilinear partial differential equations. Dynamics Reported Vol.2 (eds. U. Kirchgraber et al.), Wiley Chichester, 1989, 1–38.Google Scholar
- Y. Hosono, Singular perturbation analysis of travelling waves of diffusive Lotka-Volterra competition models. Numerical and Applied Mathematics Part II (Paris, 1988) Baltzer, Basel, 1989, 687–692.Google Scholar
- Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations. Preprint.Google Scholar